Simultaneous diophantine approximation of rational numbers
نویسندگان
چکیده
منابع مشابه
Simultaneous Diophantine Approximation
Using a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — arf < c, r(q — fir) < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals a and /3, provided that c > 1/2.6394. This improves an earlier result of Davenport, who shows that the same conclusion holds if c > 1/46"" = 1/2.6043 • • •.
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We begin by recalling some classical results on normal and nonnormal numbers. Then, we discuss the following general question. Take a property of Diophantine approximation (e.g., to be badly approximable by rational numbers, to be a Liouville number, etc.) and a property concerning the digits (e.g., to be normal, to lie in the middle third Cantor set, etc.), do there exist real numbers having b...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1972
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-22-1-1-9